Permeability of Free Space: Units & Value

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    Permeability Units
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Discussion Overview

The discussion revolves around the permeability of free space (\mu_0), its units, and its role in electromagnetism, particularly in the context of different unit systems such as SI and CGS. Participants explore the implications of defining physical constants and the historical context of unit systems.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants reference Hartle's book, which suggests that \mu_0 is treated as a pure number, while others argue that it does have units, citing external sources.
  • There is a discussion about the SI unit system, where \mu_0 is defined as \mu_0 = 4\pi \times 10^{-7} N/A², and how this relates to the introduction of the ampere as a base unit.
  • Some participants express that the SI system complicates the understanding of natural laws, suggesting that other unit systems might provide a clearer logical structure.
  • One participant mentions the historical context of the MKSA system and how it complicates units due to the inclusion of the ampere.
  • There is a mention of using natural units to simplify equations by setting fundamental constants to 1, which some participants find appealing.
  • One participant corrects a misspelling of Giorgi, who contributed to the development of the SI system.
  • A later reply emphasizes that while \mu_0 is defined as an exact number, it is not unitless in a physical sense, contrasting it with other mathematical constants like π.

Areas of Agreement / Disagreement

Participants express differing views on the nature of \mu_0, its units, and the implications of various unit systems. There is no consensus on whether \mu_0 should be considered unitless or how best to approach the definition of physical constants.

Contextual Notes

Participants note that the definitions and implications of units can vary significantly between different systems, leading to unresolved questions about the most appropriate framework for understanding electromagnetism.

PineApple2
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In Hartle's book on General Relativity, page 47 footnote 1, it says: "You might be used to thinking that quantities called [itex]\epsilon_0[/itex] and [itex]\mu_0[/itex] are the basic parameters in Maxwell's equations, but [itex]\mu_0 \equiv 4\pi \times 10^{-7}[/itex] is a pure number, and [itex]\epsilon_0 = 1/(c^2 \mu_0)[/itex]."

But as far as I know permeability of free space does have units, for example:
http://scienceworld.wolfram.com/physics/PermeabilityofFreeSpace.html
 
Last edited:
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I don't understand how this link explains the seemingly unitless permeability the textbook suggests
 
Of course these "artificial quantities" have non-unit dimension in the SI of units. The reason is that in this system of units, for electromagnetism one introduces a fourth base unit for charge (in fact in the SI it's the Ampere for the current). The magnetic permeability of the vacuum, [itex]\mu_0[/itex], is set arbitrarily to [itex]\mu_0=4 \pi \dot 10^{-7} \; \text{N}/\text{A}^2[/itex]. The dielectrical constant of the vacuum is then fixed by the relation, [itex]c^2=1/(\mu_0 \epsilon_0)[/itex], where the vacuum-speed of light is fixed within the SI by relating the unit of length (metre) to the unit of time (second) by setting its value to [itex]c=2.99792458 \cdot 10^8 \; \text{m}/\text{s}.[/itex]

From a physical point of view SI units are not very natural since electric and magnetic field components are just components of the Faraday tensor field in four-dimensional spacetime (Minkowski space in special pseudo-Riemannian space in general relativity).
 
The "electric" part of the SI system isn't perfect indeed but not worse than others.
Physicists have always tried to choose a "simple" system of units. This way, we have seen several variants of the CGS approach, where every law had its units that lead to a unitary, "simple" constant (forget the 4π that plagged those equations). Later on, people sought systems with unit speed of light, unit Planck's constant and so on.
However elegant those systems are, when time comes to measure (still an important subject in Physics) they're very complicated to live with.
I think Nature doesn't pay attention to our wishes and we will have to deal with constants (I hope not with Imperial constants)
 
Right. Of course the SI is made for everyday use and to provide well-defined units for measurement. However, when it comes to the logical structure of natural laws, other systems are better. At least [itex]\vec{E}[/itex] and [itex]\vec{B}[/itex] should have the same units and not some strange constants like [itex]\epsilon_0[/itex] and [itex]\mu_0[/itex], which are just chosen in a way to make everyday numbers in electrical engineering convenient, should appear in the equations, but the velocity of light. To also get rid of the factors [itex]4 \pi[/itex], one reationalizes the Gaussian CGS units and uses Heaviside-Lorentz units.

Of course, one can also use natural units by setting other fundamental constants to 1 (like [itex]\hbar[/itex] and/or [itex]c[/itex]) to further simplify the equations.
 
In the early part of the last century, Georgi (an electrical engineer) came to the mistaken notion that charge was a new physical unit on a par with mass, length, and time. This led eventually to the MKSA system of units, later voted into existence (in a close vote) as SI. With the purportedly 'fundamental' unit 'ampere', all SI quantities have complicated units.
If the definition of the ampere given in post #2 is used to replace 'ampere' as a unit, the SI units simplify.
 
I misspelled Giorgi.
 
PineApple2 said:
In Hartle's book on General Relativity, page 47 footnote 1, it says: "You might be used to thinking that quantities called [itex]\epsilon_0[/itex] and [itex]\mu_0[/itex] are the basic parameters in Maxwell's equations, but [itex]\mu_0 \equiv 4\pi \times 10^{-7}[/itex] is a pure number, and [itex]\epsilon_0 = 1/(c^2 \mu_0)[/itex]."

But as far as I know permeability of free space does have units, for example:
http://scienceworld.wolfram.com/physics/PermeabilityofFreeSpace.html

Your book means that it is an exact number, not that it is unit-less. It is only exact because we choose it that way, with nothing physically significant about it being exact. The number π is exact and unitless in a fundamental way independent of choice of unit system. The permeability of free space is not.
 
  • #10
+1 What @chrisbaird said :)
 

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